Moment of Inertia of Rotating Door W/ Extra Design Features

grabcad

The moment of inertia is a fundamental learning point in physics. This is because spinning is key to understanding the kinematics of our world. An objects moment of inertia can be understood as the resistance that a body exhibits to having its speed of rotation altered by a torque.An object's moment of inertia can be measured experimentally or by derivation. According to the file, RIGHT DOOR, the moment of inertia of the door about its center of mass (through the z-axis) is 38076.01 lbs*in^2. Fortunately, the moment of inertia is usually something you don't have to derive yourself because there are formulas online already. From this, we get the formula for a thin rectangular plate bout is center axis:1/12m(L^2+W^2)where m is the mass of the plate, L is the length of the plate, and W is the width of the plate.When use the values from the part and plug them into the formula, we get:1/2(60.29)(82^2+28.5^2) = 37876This is a very close approximation to the mass properties value in the SolidWorks part file. The discrepancy between the two values is partly due to the cut-extrude features on the surface of the rectangular plate. Otherwise, the approximation is accurate. In the video, however, the door rotates about it end around the hinge. According to the SolidWorks part file, the object's moment of inertia about this axis is 16350.37 (I_YY). We can determine this moment of inertia by using the parallel axis theorem, which relates the the moment of inertia about a given axis (parallel to the center of mass axes) to the moment of inertia about the center of mass, the mass of the object, and the distance between the axes:I = I_CM + Md^2The I_CM that is parallel to the moment of inertia about it end passes through the y-axis and the center of mass. According to the formula for the moment of inertia about its center of mass is:1/12(60.29)(1.5^2 + 28.5^2) = 4092.18Plugging this into the new formula:I_END = 4092.18 + (60.29)(14.25^2) = 16334.82According to SolidWorks part file, the moment of inertia about its end is 16350.37 (I_YY). Again the approximation is very close but slightly off due to the cut-extrude features on the surface of the door. NOTE: RIP Kobe Bryant